Math department of jammu and kashmir

8/9/2019 Math department of jammu and kashmir

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In 18th century mathematics isIn 18th century mathematics isalready a modern sciencealready a modern science

Mathematics begins to develop veryMathematics begins to develop veryfast because of introducing it tofast because of introducing it toschoolsschools

Therefore everyone have a chance toTherefore everyone have a chance tolearn the basic learnings oflearn the basic learnings ofmathematicsmathematics


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Thanks to that, large number of newThanks to that, large number of newmathematicians appear on stagemathematicians appear on stage

There are many new ideas, solutionsThere are many new ideas, solutions

to old mathematicalto old mathematicalproblems,researches which lead toproblems,researches which lead tocreating new fields of mathematics.creating new fields of mathematics.

Old fields of mathematics are alsoOld fields of mathematics are alsoepanding.epanding.


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!"MO#$!"MO#$M"T%&M"TI'I"($M"T%&M"TI'I"($


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LEONHARD EULERLEONHARD EULER


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Leonhard Paul EulerLeonhard Paul Euler

(1707-1783)(1707-1783) %e was a $wiss mathematician%e was a $wiss mathematician )ohann *ernoulli made the biggest)ohann *ernoulli made the biggest

influence on +eonhardinfluence on +eonhard

1- he went to $t etersburg where he1- he went to $t etersburg where heworked in the mathematics departmentworked in the mathematics departmentand became in 1/1 the head of thisand became in 1/1 the head of thisdepartmentdepartment

101 went in *erlin and worked in *erlin101 went in *erlin and worked in *erlin"cademy for - years and after that he"cademy for - years and after that hereturned in $t tersburg where he spentreturned in $t tersburg where he spentthe rest of his life.the rest of his life.


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&uler worked in almost all areas of mathematics2&uler worked in almost all areas of mathematics2geometrygeometry,, calculuscalculus,, trigonometrytrigonometry,, algebraalgebra,,appliedappliedmathematics, graph theorymathematics, graph theoryandand number theorynumber theory,,

as well as ,as well as , lunar theory, opticslunar theory, opticsand other areas ofand other areas ofphysphysicsics..

%e introduced several notational conventions in%e introduced several notational conventions inmathematicsmathematics

'oncept of a function as we use today was'oncept of a function as we use today wasintroduced by him3he was the first mathematicianintroduced by him3he was the first mathematicianto writeto write f(x)f(x) to denote functionto denote function

%e also introduced the modern notation for the%e also introduced the modern notation for thetrigonometric functionstrigonometric functions, the letter, the letter eefor the basefor the baseof theof the natural logarithmnatural logarithm4now also known as4now also known as&uler5s number&uler5s number6, the 7reek letter6, the 7reek letter forforsummations and the lettersummations and the letter iito denote theto denote theimaginary unitimaginary unit
http://en.wikipedia.org/wiki/Sigmahttp://en.wikipedia.org/wiki/Sigmahttp://en.wikipedia.org/wiki/Sigma


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%e wrote 0 books an over %e wrote 0 books an over

theses.theses. %is main book is%is main book isIntroduction inIntroduction inAnalisyis of the Infinite.Analisyis of the Infinite.


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AnalysisAnalysis

%e discovered ways to epress%e discovered ways to epressvarious logarithmic functions usingvarious logarithmic functions usingpower series, and he successfullypower series, and he successfully

defined logarithms for negative anddefined logarithms for negative andcomple numberscomple numbers

%e also defined the eponential%e also defined the eponentialfunction for comple numbers, andfunction for comple numbers, anddiscovered its relation to thediscovered its relation to thetrigonometric functionstrigonometric functions


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+&95 $ !O9M#+"+&95 $ !O9M#+"

!or any!or anyreal number real number ,,

&uler5s formula&uler5s formulastatesstates

that thethat the complecomple

eponentialeponentialfunctionfunction

ssatisfiesatisfies


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Number theoryNumber theory

%e contributed significantly to the%e contributed significantly to thetheory oftheory of perfect numbersperfect numbers, which, whichhad fascinated mathematicians sincehad fascinated mathematicians since&uclid.&uclid.

%is%isprime number theoremprime number theoremandand thethelaw oflaw of :uadratic reciprocity:uadratic reciprocity areareregarded as fundamental theoremsregarded as fundamental theorems

of number theoryof number theory..


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GeometryGeometry

&uler 41;6 showed that in any&uler 41;6 showed that in anytriangle, the orthocenter,triangle, the orthocenter,circumcenter, centroid, and nine


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Seven bridges of KonigsbergSeven bridges of Konigsberg


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This was old mathematical problem.This was old mathematical problem. The problemThe problem waswasto decide whetherto decide whether

it is possible to follow a path thatit is possible to follow a path that

crosses each bridge eactly once andcrosses each bridge eactly once andreturns to the starting point.returns to the starting point.

1/; &uler solved this problem, and1/; &uler solved this problem, and

prooved that it is not possible.prooved that it is not possible. This solution is considered to be theThis solution is considered to be the

first theorem offirst theorem of graph theorygraph theory


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&uler was very importnat for further&uler was very importnat for further

development of mathematicsdevelopment of mathematics (et :uotation tells enough about his(et :uotation tells enough about his

importance2importance2

==+ise> &uler, lise> &uler, c?est notre+ise> &uler, lise> &uler, c?est notrema@tre A tousma@tre A tous B49ead &uler, readB49ead &uler, read&uler, he is the master of us all.6&uler, he is the master of us all.6

ierre


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GABRIEL CRAMERGABRIEL CRAMER


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GABRIEL CRAMERGABRIEL CRAMER

(1704-1752)(1704-1752)

$wiss mathematician$wiss mathematician %e give the solution of $t. eterburg%e give the solution of $t. eterburg

paradoparado %e worked on analysis and%e worked on analysis and

determinantsdeterminants %e is the most famous by his rule%e is the most famous by his rule

4'ramer5s rule6 which gives a4'ramer5s rule6 which gives asolution of a system of linearsolution of a system of lineare:uations using determinants.e:uations using determinants.


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!"MA# #IMP#"$!"MA# #IMP#"$


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%e received little formal education and%e received little formal education andtaught himself mathematics while he wastaught himself mathematics while he wasworking like a weaver.working like a weaver.

$oon he became one of the most$oon he became one of the most

distinguished members of the &nglishdistinguished members of the &nglishschoolschool $impson$impsonisisbest remembered for his workbest remembered for his work

on interpolation and numerical methods ofon interpolation and numerical methods of

integration.integration. %e wrote books%e wrote booksAlgebra, Geometry,Algebra, Geometry,Trigonometry, Fluxions, Laws of ChanceTrigonometry, Fluxions, Laws of Chance,,and othersand others

!"MA# #IMP#"$!"MA# #IMP#"$

(1710-17%1)(1710-17%1)


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&EA$ LE R"$' 'ALAMBER&EA$ LE R"$' 'ALAMBER


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%e dealt with problems of dinamics%e dealt with problems of dinamicsand fluids and especially withand fluids and especially with

problem of vibrating string whichproblem of vibrating string whichleads to solving partial diferentialleads to solving partial diferentiale:uationse:uations

Curing his second part of life, he wasCuring his second part of life, he wasmainly occupied with the greatmainly occupied with the great!rench encyclopedia!rench encyclopedia

&EA$ LE R"$' 'ALAMBER&EA$ LE R"$' 'ALAMBER

(1717-1783)(1717-1783)


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!or this he wrote the introduction,!or this he wrote the introduction,and numerous philosophical andand numerous philosophical and

mathematical articles3 the best aremathematical articles3 the best arethose on geometry and onthose on geometry and onprobabilities.probabilities.


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&"#EP! L"I# LA$GRA$GE&"#EP! L"I# LA$GRA$GE


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%e didn5t show any intersts for%e didn5t show any intersts formathematics untill his 1.mathematics untill his 1.

!rom his 1, he alone threw himself!rom his 1, he alone threw himselfinto mathematical studiesinto mathematical studies

"lready with 1D, he wrote a letter to"lready with 1D, he wrote a letter to

&uler in which he solved the&uler in which he solved theisoperimetrical problem which forisoperimetrical problem which formore than half a century had been amore than half a century had been a

subEect of discussion.subEect of discussion.

&"#EP! L"I# LA$GRA$GE&"#EP! L"I# LA$GRA$GE

(173%-1813)(173%-1813)


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+agrange established a society known+agrange established a society knownas Turing "cademy, and publishedas Turing "cademy, and published

Miscellanea TaurinesiaMiscellanea Taurinesia, his work in, his work inwhich he corrects mistakes made bywhich he corrects mistakes made bysome of great mathematicianssome of great mathematicians

%e was studing problems of analytical%e was studing problems of analyticalgeometry, algebra, theory of numbers,geometry, algebra, theory of numbers,differential e:ations, mechanics,differential e:ations, mechanics,

astronomy, and many other...astronomy, and many other... (apoleon named +agrange to the(apoleon named +agrange to the

+egion of %onour and+egion of %onour and made him themade him the

'ount of the &mpire in 188.'ount of the &mpire in 188.


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On / "pril 181/ he was awarded theOn / "pril 181/ he was awarded the7rand 'roi of the Ordre ImpFrial de la7rand 'roi of the Ordre ImpFrial de la

9Funion. %e died a week later.9Funion. %e died a week later.


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PIERRE #IM"$ LAPLACEPIERRE #IM"$ LAPLACE


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!rench mathematician and astronomer!rench mathematician and astronomer %is most known works are%is most known works are Traite deTraite de

mecanique celestemecanique celeste andandTheory analytiqueTheory analytique

des probabiliteisdes probabiliteis %is name is also connected with the%is name is also connected with the=+aplace transformB and with the =+aplace=+aplace transformB and with the =+aplacee pansionB of a determinte pansionB of a determint

%e is%e is one of the first scientists to postulateone of the first scientists to postulatethe eistence ofthe eistence of black holesblack holes..

%e is one of only seventy


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It is also interesting to say theIt is also interesting to say thedifference between +aplace anddifference between +aplace and

+agrange+agrange !or +aplace, mathematics was merely!or +aplace, mathematics was merely

a kit of tools used to eplain naturea kit of tools used to eplain nature To +agrange, mathematics was aTo +agrange, mathematics was a

sublime art and was its own ecusesublime art and was its own ecusefor beingfor being


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%e is remembered%e is rememberedas one of theas one of thegreatest scientistsgreatest scientistsof all time,of all time,sometimes referredsometimes referredto as ato as a FrenchFrench

ewtonewton oror ewtonewtonof Franceof France %e became a%e became a countcount

of theof the !irst !rench!irst !rench

&mpire&mpirein 18; andin 18; andwas named awas named amar:uismar:uisin 181in 181


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GA#PAR' M"$GEGA#PAR' M"$GE


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!rench mathematician also known as!rench mathematician also known as'omte de Fluse'omte de Fluse

MongeMonge is considered the father ofis considered the father ofdifferential geometry because of hisdifferential geometry because of hisworkworkApplication de l!analyse " laApplication de l!analyse " la

g#om#trieg#om#trie where he introduced thewhere he introduced theconcept of lines of curvature of aconcept of lines of curvature of asurface in /


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%is method, which was one of%is method, which was one ofcleverly representing /


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A'RIE$ + MARIE LEGE$'REA'RIE$ + MARIE LEGE$'RE

A'RIE$ MARIE LEGE$'REA'RIE$ MARIE LEGE$'RE


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%e made important contributions to%e made important contributions tostatisticsstatistics,, number theorynumber theory,, abstractabstractalgebraalgebraandand mathematical analysismathematical analysis..

+egendre is known in the history of+egendre is known in the history ofelementary methematics principiallyelementary methematics principiallyfor his very popularfor his very popular $lements de$lements de

geometriegeometrie %e gave a simple proof that%e gave a simple proof that %%&pi'&pi'isis

irrational as well as the first proofirrational as well as the first proof

thatthat

%(%(

&pi squared'&pi squared'

is irrational.is irrational.

A'RIE$ + MARIE LEGE$'REA'RIE$ + MARIE LEGE$'RE

(1752-1833)(1752-1833)


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&&EA$EA$BBAPI#EAPI#E&&"#EP!"#EP!

,,"RIER"RIER


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!rench mathematician,!rench mathematician,physicistphysicist

and historianand historian

%e%e studied the mathematicalstudied the mathematicaltheory of heat conduction.theory of heat conduction.

&&EA$EA$BBAPI#EAPI#E&&"#EP!"#EP!,,"RIER"RIER

(17%8-1830)(17%8-1830)


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,ourer e./al.hed /he,ourer e./al.hed /he

ar/al deren/alar/al deren/al

eua/on oernn hea/eua/on oernn hea/du.on and .oled n 6du.on and .oled n 6

u.n nn/e .ere. ou.n nn/e .ere. o

/ronoe/r un/on./ronoe/r un/on.


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%%OHANNOHANN&&ARLARL''REDR&HREDR&HGGAUSSAUSS


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%%OHANNOHANN&&ARLARL''REDR&HREDR&HGGAUSSAUSS

((1777 ) 1#**1777 ) 1#**$$

%e%e worked in a wide variety of fieldsworked in a wide variety of fieldsin both mathematics and physicsin both mathematics and physicsincuding number theory, analysis,incuding number theory, analysis,

differential geometry, geodesy,differential geometry, geodesy,magnetism, astronomy and optics.magnetism, astronomy and optics.

==Mathematics is the queen of theMathematics is the queen of the

sciences and number theory is thesciences and number theory is thequeen of mathematics)queen of mathematics)**


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AG#I$ L"I# CAC!9AG#I$ L"I# CAC!9


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'auchy started the proEect of'auchy started the proEect offormulating and proving the teoremsformulating and proving the teoremsof calculus in a rigorous manner andof calculus in a rigorous manner and

was thus an early pioneer of analysiswas thus an early pioneer of analysis %e also gave several important%e also gave several important

theorems in comple analysis andtheorems in comple analysis and

initiated the study of permutationinitiated the study of permutationgroupsgroups

AG#I$ L"I# CAC!9AG#I$ L"I# CAC!9

(178*-1857)(178*-1857)


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%e also researched in convergence%e also researched in convergence

and divergence of infinite series,and divergence of infinite series,differential e:uations, determinants,differential e:uations, determinants,probability and mathematicalprobability and mathematical

physics.physics. %e was first to prove Taylor5s%e was first to prove Taylor5s

theorem, he brought a whole newtheorem, he brought a whole new

set of teorems and definitions, heset of teorems and definitions, hedealed with mechanics, optics,dealed with mechanics, optics,elasticity and many other problemselasticity and many other problems


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%is last words were2%is last words were2

Men pass away, but theirMen pass away, but their

deeds abide.deeds abide.


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Anela +ocorAnela +ocor

Matea -elu.i/Matea -elu.i/

01an -eli/01an -eli/2oisla1 3ura45o1i/2oisla1 3ura45o1i/

+oris 6o5i/+oris 6o5i/

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Math department of jammu and kashmir